Mass Transfer Effects: Immobilized and Heterogeneous Reaction Systems - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 887

The nonisothermal effects for internal diffusion limited cases can be quantified by

d C A þ

R 1

C A þ g

K b þ C A þ exp f b ¼0

f 2 ¼

1 þ b bC A þ

0

e g (17.78)

1 K b lnð1 þ K 1 Þ

b

Therefore, the impact of nonisothermal effects can be significant. Higher effectiveness factor
is obtained for higher b .
Table 17.5 shows the thermal parameters for some exothermic catalytic reaction systems.
One can observe that the value of b is commonly less than 0.2 and the range of g is between
10 and 30.
Fig. 17.8 shows the internal effectiveness factor with thermal effects for diffusion and reac-
tion in a “porous” sphere. The solid curves are numerical solutions, whereas the dashed lines
are the asymptotic solutions as given

s

2 D eA C AS
r max ;0

" Z 1 # 2

d C A þ

h ¼ f ¼ að1 þ K b Þ

C A þ g

e g

K b þ C A þ exp

(17.79)

1 þ b bC A þ

0

One can observe that the effectiveness factor can be greater than 1 for exothermic reactions
( b

0) and multiple steady states can exist at small Thiele modulus for highly exothermic
reactions.
Example 17-3. Particle size effect. A decomposition reaction is carried out on a solid
catalyst

>

A B þ C

/

over two different pellet sizes. The pellets were contained in a differential reactor that has
sufficient turbulence such that the external mass transfer effects are negligible. We know
that the adsorption coverage of A on the catalyst site is minimal and thus K A / N . The

TABLE 17.5 Thermal Parameters for Some Exothermic Catalytic Reactions

Reaction system b g

10 5

Ammonia
synthesis

6.1 29.4

10 2 Methanol

oxidation

1.1 16.0

10 2

Ethylene
hydrogenation

6.6 23.3

10 1 Benzene

hydrogenation

1.2 14.2

10 2 Sulfur dioxide

oxidation

1.2 14.8